The news follows the Government's announcement this week on Covid-19 Alert Levels, with Auckland remaining at Level 3 until this Sunday night and Wellington and the rest of the country will remain at Level 2 until Sunday 6 September.
Under Level 2 guidelines, the Steinlager North v South match will have to be played with no crowd in attendance.
NZR General Manager Professional Rugby & Performance Chris Lendrum said: "We're delighted that the match can go ahead in Wellington, but obviously it's a shame that it'll have to be played without fans in the stands. That said, we're fully supportive and understanding of the Government's health and safety recommendations regarding Covid-19."
The match was originally scheduled for Eden Park on 29 August and fans who bought tickets to the match will be refunded via ticketing agency Ticketmaster.
"We feel for the Auckland fans who were set to fill Eden Park in their tens of thousands. If we have that same response from fans watching the match on TV, then it will be a huge audience tuning in on Sky," Lendrum said.
The match is scheduled to kick off at 7.10PM on Saturday 5 September, live and exclusive on Sky Sport.
The North and South squads will assemble in Wellington on Monday to prepare for the match.
Meanwhile, the Farah Palmer Cup and Mitre 10 Cup competitions will go ahead as scheduled, with the Farah Palmer Cup kicking off on Saturday 5 September and the Mitre 10 Cup the following weekend.